Question

Plane harmonic waves of frequency $500Hz$ are produced in the air with a displacement amplitude of $10$ $\mu$ m. Given that the density of air is $1.29kg/m$${}^3$ and the speed of sound in air is $340m/s$. Then

• A. the pressure amplitude is $13.8N/m^2$
• B. the energy density is $6.4\times {10}^{-4}J/m^3$
• C. the energy flux is $0.22J/(m^2$ s)
• D. only (a) and (c) are correct

Answer 1

Answer: (A), (B)

the pressure amplitude is $13.8N/m^2$
the energy density is $6.4\times {10}^{-4}J/m^3$

We know that

$v=\sqrt{\frac{B}{P}}⟹v^{2}P=B$(Bulk modulus)

$(340{)}^2\times 1.29=149124=B$

$v=\nu \lambda$

$\frac{340}{500}=\lambda =0.68$ and $K=\frac{2\pi }{\lambda }=9.23$

Pressure amplitude=$BAK$

$⟹149124\times (10\times {10}^{-6}\times 9.23)$

$⟹13.8N/m^2$

Energy density=$\frac{1}{2}P{w}^2{A}^2$

$⟹\frac{1}{2}\times 1.29\times (2\pi \times 500{)}^2\times (10\times {10}^{-6}{)}^2$

$(w=2\pi f⟹2\pi \times 500)$

$⟹6.4\times {10}^{-4}J/m^3$